2001 Battery Drain question... I've checked all the forums already...

[Allstarsrd12]

K, first just need to state that I've done extensive amount of searching and forum digging before I posted this.
here is the situation. Car has been sitting for about 3 months. Started fine always before.
Came back, tried to jump it, no go. high beams flickered, clicking noise, etc.
Called AAA, came and put the big battery pack thing on, it started on the first crank. Rules our solenoid and starter.
Ran for about an hour, drove around a little bit, turned it off. Wouldn't turn back on, same thing. Called AAA again, jumped right up with their battery pack. Did a meter testing and said the battery was WEAK, not just GOOD or BAD. Guy said its maybe the alternator.
Checked the records, alternator was replaced sept. 2008 by BMW.
Question is, is it just that certainly just need to get a new battery, and test it out and see if there is an electrical situation with something staying on?
OR
Is it that and the final stage resistor/unit, the gear shift light problem (which many say is not a real factor), or maybe the CD changer problem.
OR
Is it just the alternator...

One more note. After AAA jumped it the first time, when I put it back and forth between drive and park, it almost seemed to slightly want to stall, and was just acting a little funny.

ANY inputs would be GREATLY appreciated. Thanks so much. This is my first BMW, and I just want to drive it!!!

Steve